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Abstract

Highly directional radiation from photonic structures is important for
many applications, including high-power photonic crystal
surface-emitting lasers, grating couplers, and light detection and
ranging devices. However, previous dielectric, few-layer designs only
achieved moderate asymmetry ratios, and a fundamental understanding of
bounds on asymmetric radiation from arbitrary structures is still
lacking. Here, we show that breaking the 180° rotational
symmetry of the structure is crucial for achieving highly asymmetric
radiation. We develop a general temporal coupled-mode theory formalism
to derive bounds on the asymmetric decay rates to the top and bottom
of a photonic crystal slab for a resonance with arbitrary in-plane
wavevector. Guided by this formalism, we show that infinite asymmetry
is still achievable even without the need for back-reflection mirrors,
and we provide numerical examples of designs that achieve asymmetry
ratios exceeding 104. The emission direction can also be
rapidly switched from top to bottom by tuning the wavevector or
frequency. Furthermore, we show that with the addition of weak
material absorption loss, such structures can be used to achieve
perfect absorption with single-sided illumination, even for
single-pass material absorption rates less than 0.5% and without
back-reflection mirrors. Our work provides new design principles for
achieving highly directional radiation and perfect absorption in
photonics.

Figures (4)

Temporal coupled-mode theory setup and transmission spectrum.
(a) Schematic of our TCMT setup with four ports and two resonances
related by the time-reversal operation. This general setup is
valid for structures with arbitrary shapes and incident angles as
long as the assumption of four ports and two resonances is
correct. (b) Typical transmission spectrum of an
inversion-symmetric, C2z-symmetry-broken structure, with
the Fano resonances exhibiting full transmission at certain
frequencies as predicted by our TCMT formalism. Strong asymmetry
is achieved when the Fano resonance is aligned with the
frequencies where the background reaches full transmission (red
circles).

Simulated structures and verification of TCMT bounds. (a) The
P-symmetric structure we use in our
numerical examples and its structural parameters.
a: periodicity of photonic crystal,
h: height of central slab,
w: width of central slab,
n0: refractive index of central
slab, d: height of additional pieces on
the sides (the width of the additional pieces is
(a−w)/2), nd: refractive index of additional
pieces on the sides; (b) numerical verification of TCMT bounds on
asymmetric radiation for P-symmetric structures. Red lines
indicate the bound from Eq. (11). Each blue cross indicates simulation
results of the asymmetry for a given structure, optimized over
in-plane momentum. The transmissivity t is fitted from the Fabry–Perot
background, and the asymmetric coupling ratio is calculated from
the Poynting flux in the top and bottom directions.

Examples of highly asymmetric radiation. (a) Plot of the asymmetry
ratio and quality factor as a function of
kx, along the
ky=0 axis in momentum space. Strong
asymmetric radiation occurs over a range of momenta, including the
point of highest quality factor. Inset: log scale plot of the
z-component of the electric field
amplitude at the highest asymmetry point. (b) Similar plot for a
different set of parameters, showing rapid switching of asymmetric
direction by tuning the frequency or in-plane momentum.

Perfect absorption with single-sided illumination and no backing
mirror for single-pass absorption less than 0.5%. (a) Schematic
for perfect absorption at one incident angle and perfect
transmission at the opposite incident angle. (b) Transmission,
reflection, and absorption spectra for no loss
(Qnr=∞) and critical loss
(Qnr=Qr), consistent with the theoretical
results in (a). (c) Loss dependence of absorption, showing
near-perfect absorption for critical coupling.